9) The Wronskian of the functions f(x) = -5, g(æ) = 7x² y h(x) = e3 is given by a) W(f(x), g(x), h(æ)) = 42(3x – 1)e** b) W(f(æ), 9(x), h(x)) = -210(3x – 1)ez c) W(f(x), g(x), h(x)) = 42(1 – 3æ)e
Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…
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A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1
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A: Given
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A: Part (a): (i) Find derivative of x and y. (ii) Equate to zero, to get critical points.
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A: (1,1) is the local minimum point explanation is given in below step
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A:
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- f(x) = (x2-x-1) e-x is restricted to the domain x ≥ 0 and it has two critical points. One at x = 0 and the other at x = 3 At what value x does f(x) attain its maximum?2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?Maximize f(x) = 4x 1.8x² + 1.2x³- 0.3x4 a) Using Golden-Section Search (x₁ = −2,xu = 4, εs = 1%) b) Using Newton's Method (xo = 3, &s=1%)
- The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1 (A) How many critical points does ff have in R2R2? (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. (E) What is the maximum value of ff on R2R2? If there is none, type N. (F) What is the minimum value of ff on R2R2? If there is none, type N.Consider the function f(x) =-5x^2+8x-8 F(x) has a critical point at x=A
- A first order nonlinear system is described by the equationẋ = −f(x)where f(x) is a continuous and differentiable nonlinear function thatsatisfies the following:f(0) = 0;f(x) > 0 for x > 0;f(x) < 0 for x < 0.Use the Lyapunov function V(x) = x2/2 to show that the system isstable near the origin.Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the linearization to estimate the value of f(2.1).13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]
- Let y : R → R be the real-valued function defined on the real line, which is the solution of the initialvalue problemy' = −xy + x, y(0) = 2.Which statements are correct?a) The problem is not uniquely solvable.b) The solution y(x) contains an exponential function.c) limx→∞ y(x) = 1d) limx→∞ y(x) = 0The leading behavior h(infinity)(x) for h(x) = (1.3x+(x^3.2)+(e^2.4x))/(1.3+3.2x+(2.4x^2)) at infinity is h(infinity)(x) =A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.